A machine fired several projectiles at the same angle, θ, above the horizontal. Each projectile was fired with a different initial velocity, vi. The graph below represents the relationship between the magnitude of the initial vertical velocity, viy, and the magnitude of the corresponding initial velocity, vi, of these projectiles.

51. Determine the magnitude of the initial vertical velocity of the projectile, viy, when the magnitude of its initial velocity, vi, was 40. meters per second. [1]

52. Determine the angle, θ, above the horizontal at which the projectiles were fired. [1]

53. Calculate the magnitude of the initial horizontal velocity of the projectile, vix, when the magnitude of its initial velocity, vi, was 40. meters per second. [Show all work, including the equation and substitution with units.] [2]

54. A student makes a simple pendulum by attaching a mass to the free end of a 1.50-meter length of string suspended from the ceiling of her physics classroom. She pulls the mass up to her chin and releases it from rest, allowing the pendulum to swing in its curved path. Her classmates are surprised that the mass doesn’t reach her chin on the return swing, even though she does not move. Explain why the mass does not have enough energy to return to its starting position and hit the girl on the chin. [1]

55. A 6-ohm resistor and a 4-ohm resistor are connected in series with a 6-volt battery in an operating electric circuit. A voltmeter is connected to measure the potential difference across the 6-ohm resistor.

In the space in your answer booklet, draw a diagram of this circuit including the battery, resistors, and voltmeter using symbols from the Reference Tables for Physical Setting/Physics. Label each resistor with its value. [Assume the availability of any number of wires of negligible resistance.] [2]

56. When a spring is compressed 2.50 x 10–2 meter from its equilibrium position, the total potential energy stored in the spring is 1.25 x 10–2 joule. Calculate the spring constant of the spring. [Show all work, including the equation and substitution with units.] [2]

Refer to the following information for the next two questions.

A 3.50-meter length of wire with a cross- sectional area of 3.14 x 10–6 meter2 is at 20° Celsius. The current in the wire is 24.0 amperes when connected to a 1.50-volt source of potential difference.

57. Determine the resistance of the wire. [1]

58. Calculate the resistivity of the wire. [Show all work, including the equation and substitution with units.] [2]

Refer to the following information for the next two questions.

In an experiment, a 0.028-kilogram rubber stopper is attached to one end of a string. A student whirls the stopper overhead in a horizontal circle with a radius of 1.0 meter. The stopper completes 10. revolutions in 10. seconds.

59. Determine the speed of the whirling stopper. [1]

60. Calculate the magnitude of the centripetal force on the whirling stopper. [Show all work, including the equation and substitution with units.] [2]

Refer to the following information for the next four questions.

In a laboratory investigation, a student applied various downward forces to a vertical spring. The applied forces and the corresponding elongations of the spring from its equilibrium position are recorded in the data table below.

61. Mark an appropriate scale on the axis labeled “Force (N).” [1]

62. Plot the data points for force versus elongation. [1]

63. Draw the best-fit line or curve. [1]

64. Using your graph, calculate the spring constant of this spring. [Show all work, including the equation and substitution with units.] [2]

Refer to the following information for the next four questions.

An ice skater applies a horizontal force to a 20.-kilogram block on frictionless, level ice, causing the block to accelerate uniformly at 1.4 meters per second2 to the right. After the skater stops pushing the block, it slides onto a region of ice that is covered with a thin layer of sand. The coefficient of kinetic friction between the block and the sand-covered ice is 0.28.

65. Calculate the magnitude of the force applied to the block by the skater. [Show all work, including the equation and substitution with units.] [2]

66. On the diagram in your answer booklet, starting at point A, draw a vector to represent the force applied to the block by the skater. Begin the vector at point A and use a scale of 1.0 centimeter = 5.0 newtons. [1]

67. Determine the magnitude of the normal force acting on the block. [1]

68. Calculate the magnitude of the force of friction acting on the block as it slides over the sand-covered ice. [Show all work, including the equation and substitution with units.] [2]

Refer to the following information for the next three questions.

A monochromatic light ray (f = 5.09 × 1014 Hz) traveling in air is incident on the surface of a rectangular block of Lucite.

69. Measure the angle of incidence for the light ray to the nearest degree. [1]

70. Calculate the angle of refraction of the light ray when it enters the Lucite block. [Show all work, including the equation and substitution with units.] [2]

71. What is the angle of refraction of the light ray as it emerges from the Lucite block back into air? [1]

Refer to the following information for the next four questions.

As a mercury atom absorbs a photon of energy, an electron in the atom changes from energy level d to energy level e.

72. Determine the energy of the absorbed photon in electronvolts. [1]

73. Express the energy of the absorbed photon in joules. [1]

74. Calculate the frequency of the absorbed photon. [Show all work, including the equation and substitution with units.] [2]

75. Based on your calculated value of the frequency of the absorbed photon, determine its classification in the electromagnetic spectrum. [1]